ho hasn’t dreamed about being
invisible? How wonderful it
would be to slip under a magic
cloak and sneak away unseen on exciting
adventures. Invisibility has appeared in count-
less works of fiction, from legends of the ancient
Greeks and Germans to Harry Potter. Yet it
is only recently that invisibility has become a
respectable area of science.
A little more than five years ago, the first
peer-reviewed scientific papers with ideas for
invisibility cloaking were published, followed
by the first demonstration of a simple cloaking device for microwaves. I wrote one of those
papers and remember very well how di;cult
it was to get it published; it was rejected many
times. Since then scientific research on invisibility has exploded. In December 2010, Science
listed these new tricks with light as one of the
top 10 research insights of the last decade. ;ey
have the potential to significantly change the fields of optics
and photonics in the near future.
Herbert Wells’ The Invisible
Man makes himself invisible by
changing every cell in his body,
giving it the same refractive
index as air.
In the Fantastic Four, Susan Storm (the
Invisible Woman) has a less destructive way
of achieving invisibility. She manipulates her
surroundings instead of changing herself.
Susan deploys a mysterious force field that
curves space and bends light around her.
Outside the force field, light rays travel in
straight lines, but when they enter the field
they bend around her and then continue
along their original straight paths. Since
light goes around Susan, she is hidden from
view. In reality, however, no mysterious force
field is needed for curving space and bending
light. ;is trick can be accomplished by using
advanced optical materials.
Invisibility in pop culture
Two fictional stories serve rather well in illustrating di;erent
approaches for invisibility; Herbert Wells’ novel ;e Invisible
Man and the Invisible Woman from the comic book and
movie Fantastic Four.
In Wells’ novel, Gri;n (the invisible man) is a disgruntled
chemistry professor at a provincial college. He invents a
substance that gives every cell in his body the refractive index
of air. He becomes optically indistinguishable from air, which
makes him transparent. Other characters in the book literally see right through him. To achieve this state, Gri;n had
to make drastic, irreversible changes to himself, and the novel
ends in catastrophe.
Some generals dream of invisible tanks.
Phil Saunders, spacechannel.org
In 1662, an amateur scientist and politician
named Pierre de Fermat wrote a letter about
what was to be known as Fermat’s principle. Fermat was an
eminent and enigmatic mathematician who loved teasing his
colleagues with cryptic remarks about important mathemati-
cal insights that he found without explaining them. He also
made some discoveries in optics. Fermat’s principle states that
when light travels from one point to another it always follows
the shortest optical path. In empty space, the shortest path
is a straight line, but materials change the speed of light by
their refractive index profiles. If the refractive index varies, the
shortest path through the material is no longer a straight line.
Light will preferentially propagate where it is relatively fast
(where the refractive index is low) and avoid regions of high
Fermat’s principle explains why light rays are bent in
optical materials; they follow the shortest paths. In this case,
“short” can have two meanings—“shortest time” or “shortest
length.” You can take a measurement of time, multiply it by
the speed of light in a vacuum and get a measure of length.
In fact, this is how length is defined in SI units. ;erefore,
an optical material that changes the speed of light by its
refractive index changes the measure of length. For example,
a region of high refractive index appears to be longer than a
;is takes us straight to the geometry of curved space. ;e
word “geometry” means “Earth measurement,” which remains
almost literally true in modern mathematics where the measure
of length incorporates everything about the geometry of space.
In general, this space is curved.
If you use Fermat’s principle, optical materials appear to
curve space. ;ere are two geometries to consider: the
ordinary geometry of physical space and the virtual
geometry conjured up by the optical material—
the geometry of a virtual space.
;is is probably best explained
by using a fish tank as an
32 | OPN Optics & Photonics News